Question: What's the first wrong statement in the proof below that $ \triangle BCE \cong \triangle BCA$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{BC} \cong \overline{BD}$ $, \ $ $ \angle ABC \cong \angle DBE$ $, \ $ $ \angle BAC \cong \angle BED$ $, \ $ $ \overline{AB} \cong \overline{EF}$ $, \ $ $ \angle BAC \cong \angle CEF$ $, \ $ and $\ $ $ \angle ACB \cong \angle ECF$ Proof $ \triangle BDE \cong \triangle BCA$ because AAS $ \overline{BE} \cong \overline{AB}$ because corresponding parts of congruent triangles are congruent $ \triangle BDE \cong \triangle FCE$ because ASA $ \angle ACB \cong \angle BDE$ because corresponding parts of congruent triangles are congruent $ \triangle BCA \cong \triangle FCE$ because AAS $ \triangle BCE \cong \triangle BCA$ because SSS
Explanation: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \triangle FCE \cong \triangle BDE$ is the first wrong statement.